It has been reported that approximately 360,000 open heart procedures were performed in 1983 and approximately 25 percent used a disposable membrane oxygenator. As open heart procedures become more complex, entailing higher risks, it is anticipated that membrane oxygenators will be utilized more often. The present invention is directed to an inexpensive, atraumatic, hemocompatible, pulsatile diaphragm pump that can be used for cardiopulmonary bypass and replace the conventional blood roller pump which after a time period causes blood trauma. The present pump, because of its qualities, is useful for use with membrane oxygenators. Present blood pumps are extremely expensive, use clinical heart valves which cost as much as $2,500 per valve, and still are thrombogenic. The present blood pump uses simple leaf valves that are integral in a pumping chamber and molded as part of the chambers to provide an inexpensive, disposable atraumatic pump which can be used for heart surgery, post operative support and other uses.